MACS 40700
University of Chicago
\[Y = \beta_0 + \beta_{1}X\]
##
## Call:
## lm(formula = y ~ x, data = sim1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.147 -1.520 0.133 1.467 4.652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.221 0.869 4.86 4.1e-05 ***
## x 2.052 0.140 14.65 1.2e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.2 on 28 degrees of freedom
## Multiple R-squared: 0.885, Adjusted R-squared: 0.88
## F-statistic: 215 on 1 and 28 DF, p-value: 1.17e-14
\[\text{Influence} = \text{Leverage} \times \text{Discrepancy}\]
Leverage statistic/hat value
\[h_i = \frac{1}{n} + \frac{(x_i - \bar{x})^2}{\sum_{i'=1}^{n} (x_{i'} - \bar{x})^2}\]
Cook’s D
## Cell Contents
## |-------------------------|
## | Count |
## | Total Percent |
## |-------------------------|
##
## =======================================
## happy$sex
## happy$happy male female Total
## ---------------------------------------
## not too happy 1904 2460 4364
## 5.5% 7.1%
## ---------------------------------------
## pretty happy 8760 10539 19299
## 25.2% 30.3%
## ---------------------------------------
## very happy 4833 6327 11160
## 13.9% 18.2%
## ---------------------------------------
## Total 15497 19326 34823
## =======================================
## Cell Contents
## |-------------------------|
## | Count |
## | Row Percent |
## |-------------------------|
##
## =======================================
## happy$sex
## happy$happy male female Total
## ---------------------------------------
## not too happy 1904 2460 4364
## 43.6% 56.4% 12.5%
## ---------------------------------------
## pretty happy 8760 10539 19299
## 45.4% 54.6% 55.4%
## ---------------------------------------
## very happy 4833 6327 11160
## 43.3% 56.7% 32.0%
## ---------------------------------------
## Total 15497 19326 34823
## =======================================
## Cell Contents
## |-------------------------|
## | Count |
## | Column Percent |
## |-------------------------|
##
## =======================================
## happy$sex
## happy$happy male female Total
## ---------------------------------------
## not too happy 1904 2460 4364
## 12.3% 12.7%
## ---------------------------------------
## pretty happy 8760 10539 19299
## 56.5% 54.5%
## ---------------------------------------
## very happy 4833 6327 11160
## 31.2% 32.7%
## ---------------------------------------
## Total 15497 19326 34823
## 44.5% 55.5%
## =======================================
## Cell Contents
## |-------------------------|
## | Count |
## | Row Percent |
## | Column Percent |
## |-------------------------|
##
## =======================================
## happy$sex
## happy$happy male female Total
## ---------------------------------------
## not too happy 1904 2460 4364
## 43.6% 56.4% 12.5%
## 12.3% 12.7%
## ---------------------------------------
## pretty happy 8760 10539 19299
## 45.4% 54.6% 55.4%
## 56.5% 54.5%
## ---------------------------------------
## very happy 4833 6327 11160
## 43.3% 56.7% 32.0%
## 31.2% 32.7%
## ---------------------------------------
## Total 15497 19326 34823
## 44.5% 55.5%
## =======================================
| var | mean | sd | min | max | n |
|---|---|---|---|---|---|
| DiscCH | 0.052 | 0.117 | 0.00 | 0.500 | 1070 |
| DiscMM | 0.123 | 0.214 | 0.00 | 0.800 | 1070 |
| LoyalCH | 0.566 | 0.308 | 0.00 | 1.000 | 1070 |
| PctDiscCH | 0.027 | 0.062 | 0.00 | 0.253 | 1070 |
| PctDiscMM | 0.059 | 0.102 | 0.00 | 0.402 | 1070 |
| PriceCH | 1.867 | 0.102 | 1.69 | 2.090 | 1070 |
| PriceMM | 2.085 | 0.134 | 1.69 | 2.290 | 1070 |
| SalePriceCH | 1.816 | 0.143 | 1.39 | 2.090 | 1070 |
| SalePriceMM | 1.962 | 0.253 | 1.19 | 2.290 | 1070 |
| SpecialCH | 0.148 | 0.355 | 0.00 | 1.000 | 1070 |
| SpecialMM | 0.162 | 0.368 | 0.00 | 1.000 | 1070 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 49.24 | 1.858 | 26.51 | 0 |
| displ | -11.76 | 1.073 | -10.96 | 0 |
| I(displ^2) | 1.09 | 0.141 | 7.77 | 0 |
| (1) | (2) | (3) | (4) | |
| Engine displacement | -11.800*** | -11.200*** | -7.150*** | -3.710*** |
| (1.070) | (1.410) | (1.220) | (1.280) | |
| Engine displacement^2 | 1.090*** | 1.060*** | 0.686*** | 0.381*** |
| (0.141) | (0.153) | (0.130) | (0.135) | |
| Number of cylinders | -0.264 | -0.746** | -1.040*** | |
| (0.411) | (0.343) | (0.315) | ||
| Front wheel drive | 4.520*** | 2.770*** | ||
| (0.496) | (0.619) | |||
| Rear wheel drive | 4.180*** | 1.170 | ||
| (0.686) | (0.734) | |||
| Compact | -2.780* | |||
| (1.510) | ||||
| Midsize | -2.630* | |||
| (1.550) | ||||
| Minivan | -6.500*** | |||
| (1.720) | ||||
| Pickup | -7.380*** | |||
| (1.470) | ||||
| Subcompact | -2.230 | |||
| (1.470) | ||||
| SUV | -6.560*** | |||
| (1.370) | ||||
| Constant | 49.200*** | 49.300*** | 40.800*** | 40.300*** |
| (1.860) | (1.860) | (1.750) | (2.050) | |
| Observations | 234 | 234 | 234 | 234 |
| R2 | 0.672 | 0.673 | 0.782 | 0.838 |
| Adjusted R2 | 0.670 | 0.669 | 0.778 | 0.830 |
| Residual Std. Error | 3.420 (df = 231) | 3.430 (df = 230) | 2.810 (df = 228) | 2.450 (df = 222) |
| F Statistic | 237.000*** (df = 2; 231) | 158.000*** (df = 3; 230) | 164.000*** (df = 5; 228) | 105.000*** (df = 11; 222) |
| Note: | p<0.1; p<0.05; p<0.01 | |||
| PassengerId | Survived | Pclass | Name | Sex | Age | SibSp | Parch | Ticket | Fare | Cabin | Embarked |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 3 | Braund, Mr. Owen Harris | male | 22 | 1 | 0 | A/5 21171 | 7.25 | S | |
| 2 | 1 | 1 | Cumings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38 | 1 | 0 | PC 17599 | 71.28 | C85 | C |
| 3 | 1 | 3 | Heikkinen, Miss. Laina | female | 26 | 0 | 0 | STON/O2. 3101282 | 7.92 | S | |
| 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel) | female | 35 | 1 | 0 | 113803 | 53.10 | C123 | S |
| 5 | 0 | 3 | Allen, Mr. William Henry | male | 35 | 0 | 0 | 373450 | 8.05 | S | |
| 6 | 0 | 3 | Moran, Mr. James | male | NA | 0 | 0 | 330877 | 8.46 | Q |
## term estimate std.error statistic p.value
## 1 (Intercept) -0.0567 0.17358 -0.327 0.7438
## 2 Age -0.0110 0.00533 -2.057 0.0397
| (1) | (2) | (3) | |
| Age | -0.011** | -0.005 | 0.020* |
| (0.005) | (0.006) | (0.011) | |
| Male | -2.470*** | -1.320*** | |
| (0.185) | (0.408) | ||
| Age x Male | -0.041*** | ||
| (0.014) | |||
| Constant | -0.057 | 1.280*** | 0.594* |
| (0.174) | (0.230) | (0.310) | |
| Observations | 714 | 714 | 714 |
| Log Likelihood | -480.000 | -375.000 | -370.000 |
| Akaike Inf. Crit. | 964.000 | 756.000 | 748.000 |
| Note: | p<0.1; p<0.05; p<0.01 | ||